Quilting is usually personal preference so you will get lots of opinions.
1. I like to pull my thread tails up, knot them and using a easy thread needle to bury them in the quilt sandwich. Some people do like to do tiny stitches to lock the ends of the thread instead of knotting.
2.You can quilt the border along with the quilt if you want or do it separately, it's up to you.
3.If this is your first try at machine quilting then using your walking foot and doing straight lines will probably be easiest.
Make sure your sandwich is basted well before starting to quilt. Some people like 505 basting spray, some like safety pin basting, some like needle and thread basting. You should be able to find videos on basting on Youtube.